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**Create the page "Prime-parametrized group properties" on this wiki!** See also the search results found.

- The Group Properties Wiki is designed and organized using a property-theoretic paradigm. This ar Examples from group theory:7 KB (1,067 words) - 22:24, 7 May 2008
- ...ties over structures and the algebraic and logical relations between those properties'' Examples from group theory:4 KB (575 words) - 22:44, 7 May 2008
- This is an informal account of the story of the development of the Group Properties Wiki, till 2007. The '''Group Properties Wiki''', called ''groupprops'' first began life at2 KB (398 words) - 22:44, 7 May 2008
- ...lves whatever problem we are considering in terms of oracle queries to the group operations and any pre-processing or post-processing that needs to be done. Any black-box group algorithm gives an actual algorithm if we are actually provided an encoding2 KB (408 words) - 07:21, 21 December 2014
- ...nsion <math>F</math> over <math>\mathbb{Q}</math> satisfying the following properties. Let <math>I</math> denote the ring of algebraic integers in <math>F</math>2 KB (401 words) - 23:12, 7 May 2008
- An element of a [[group]] is termed central if the following equivalent conditions hold: # It commutes with every element of the group15 KB (2,081 words) - 20:14, 1 June 2016
- Let <math>\sigma</math> be an automorphism of a group <math>G</math>. We say that <math>\sigma</math> is '''characteristic-semidi ===Stronger properties===1 KB (150 words) - 15:44, 8 April 2009
- A [[subgroup]] of a [[group]] is termed a '''characteristic direct factor''' if it is a [[characteristi * Every group is a characteristic direct factor of itself.4 KB (455 words) - 02:59, 20 January 2013
- ...core]] is a [[defining ingredient::characteristic subgroup]] of the whole group. A [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed '''core-characteristic''' if the normal core <ma3 KB (285 words) - 17:34, 21 December 2014
- A prime divisor of a number is said to be '''core-nontrivial''' if for every group whose order is that number, the core for that prime divisor is nontrivial. ...nontrivial''' if for any group <math>G</math> of order <math>N</math>, the group <math>O_p(G)</math> (viz the <math>p</math>-core of <math>G</math>) is nont2 KB (413 words) - 23:24, 7 May 2008
- {{prime-parametrized sdf}} Let <math>G</math> be a [[finite group]] of order <math>N</math> and let <math>p</math> be a prime divisor of <mat2 KB (287 words) - 23:24, 7 May 2008
- A family <math>\mathcal{F}</math> of subgroups of a group <math>G</math> is termed a '''cover''' for <math>G</math> if it satisfies t ==Properties==876 bytes (150 words) - 23:24, 7 May 2008
- {{nottobeconfusedwith|[[critical group]]}} ...bgroup''' if it is [[characteristic subgroup|characteristic]] in the whole group and satisfies the following three conditions:4 KB (489 words) - 00:05, 13 February 2009
- {{pivotal group property}} {{natural number-parametrized group family}}8 KB (1,111 words) - 23:25, 20 June 2013
- {{particular group}} ...ined as the unique group of order two. Explicitly it can be described as a group with two elements, say <math>e</math> and <math>x</math> such that <math>ex8 KB (1,234 words) - 05:31, 21 January 2013
- {{particular group}} ...ined as the unique group of order 3. Equivalently it can be described as a group with three elements <math>e= x^0,x,x^2</math> where <math>x^lx^m = x^{l+m}<6 KB (839 words) - 04:07, 12 January 2013
- {{prime set-parametrized group property}} Let <math>G</math> be a [[finite group]], and <math>\pi</math> be a set of primes. We say that <math>G</math> sati821 bytes (134 words) - 23:25, 7 May 2008
- {{nottobeconfusedwith|[[dicyclic group]] (also called binary dihedral group)}} {{group property}}10 KB (1,448 words) - 02:22, 6 July 2019
- {{particular group}} ...times the ''octic group'', is defined by the following [[presentation of a group|presentation]], with <math>e</math> denoting the identity element:19 KB (2,660 words) - 13:15, 14 February 2015
- ...up correlates with the way the normal subgroups are distributed within the group? This, and other related questions, are explored within this article. ! Group !! Order !! Orders of normal subgroups (with multiplicity) !! Indexes of no11 KB (1,600 words) - 23:24, 3 November 2010